On the Kobayashi-Hitchin correspondence for Kähler currents
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912727749885952 |
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| author | Jinnouchi, Satoshi |
| author_facet | Jinnouchi, Satoshi |
| contents | In this paper, we show that if a holomorphic vector bundle is slope polystable with respect to a Kähler class, then it admits a Hermitian-Yang-Mills metric with respect to a suitable Kähler current with singularities in higher codimension which represents the Kähler class. Most parts of the proof remains valid for closed positive $(1,1)$-currents representing a nef and big class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20033 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Kobayashi-Hitchin correspondence for Kähler currents Jinnouchi, Satoshi Differential Geometry 53C07, 32W20 In this paper, we show that if a holomorphic vector bundle is slope polystable with respect to a Kähler class, then it admits a Hermitian-Yang-Mills metric with respect to a suitable Kähler current with singularities in higher codimension which represents the Kähler class. Most parts of the proof remains valid for closed positive $(1,1)$-currents representing a nef and big class. |
| title | On the Kobayashi-Hitchin correspondence for Kähler currents |
| topic | Differential Geometry 53C07, 32W20 |
| url | https://arxiv.org/abs/2511.20033 |